A triangle has corners A, B, and C located at #(7 ,3 )#, #(4 ,8 )#, and #(3 , 4 )#, respectively. What are the endpoints and length of the altitude going through corner C?

1 Answer
Feb 3, 2016

Answer:

The answer is (5.5,5.5)

Explanation:

this an isosceles triangle, you can show it by calculating the
#AC = BC #
distance formula #sqrt((x_2-x_1)^2 + (y_2-y_1)^2)#
Thus:
# sqrt(4^2+1^2) = 4.123#
#sqrt (1^2+4^2) = 4.123#
So the midpoint of the base should be the altitude since it will also be the perpendicular bisector.
Now subtracting point A from B
You will find the horizontal a d vertical separation to be (3,-5)
half these separation, (1.5, -2.5), add to B(4,8) or subtract fromA(7, 3)
And get the point (5.5,5.5) this is the altitude of our isosceles triangle...